الفهرس 
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Abstract
We note that all the mathematical concepts which are introduced in this introduction will be defined later.
Stochastic optimal control (SOC) is a mix between a stochastic differential equation (SDE) NOTE its solution by u; and a functional with two parameters u; and the control law. SOC was studied by several authors (see[5], [81] and [64]) and numerical method (see[74]and [9]). This thesis is devoted to study an important type of SOC in which the SDE is a stochastic Heat Equation (SHE); this last is a particular case of the stochastic partial Differential Equation (SPDE).